The father of a Sydney teenager murdered by her boyfriend has told the New South Wales Supreme Court her death was irrational and incomprehensible.

Jazmin-Jean Ajbschitz, 18, was bashed to death by Sean Lee King at her mother's Ultimo apartment in July 2011.

In a victim impact statement read to his sentencing hearing her father Shlomo Sol Ajbschitz, the son of Holocaust survivors, said he considered Australia to be "paradise" when he moved here from Israel.

But he said 40 years of healing had been undone in one brutal act.

Ms Ajbschitz's mother and two brothers described her as beautiful, talented and a loss to her friends, family and community.

In his address to the court, King said he was ashamed of his crime and asked the family for forgiveness.

King told the victim's family he was sorry for taking their beautiful girl.

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